Problem 1: Your firms research department has estimated your total revenues to be: R (Q) = 3,000Q – 8Q2 and your total costs to be C (Q) = 100 + 2Q2.
Calculate the marginal benefit and marginal cost functions.
a. What level of Q maximizes net benefits?
b. What is marginal benefit at this level of Q?
c. What is the marginal cost at this level of Q?
d. What is the maximum level of net benefits?
e. What is another word for “Net benefits” in this example?
Problem 2: GGH recently instituted an in-house recycling program. The benefits of this program include not only the benefits to the environment of recycling but also the goodwill generated by GGH’s leadership in this area. The costs of recycling include all the energy, labor, and space to do the recycling. Suppose these benefits and costs are given by: B (Q) = 100Q – 2Q2 and C (Q) = 2Q.
Calculate the marginal benefit and marginal cost functions.
a. What level of Q maximizes the total benefits of reclying?
b. What level of Q minimizes the total costs of recycling?
c. What level of Q maximizes the net benefits of recycling?
d. What level of recycling is optimal? Why?
Problem 3: Fuji Software, Inc. has the two following mutually exclusive projects with their respective cash flows.
Year Project A Project B
0 - $ 7,500 - $ 5,000
1 4,000 2,500
2 3,500 1,200
3 1,500 3,000
Using the net present value rule to rank these two projects, what project should be chosen if the discount rate is 15%? What if the discount rate was 9%?
Problem 4: You have been hired to replace the manager of a firm that used only two inputs, capital and labor, to produce output. The firm can hire as much labor as it wants at a wage of $5 per hour and can rent as much capital as it wants at a price of $50 per hour. After you look at the company’s books, you learn that the company has been using capital and labor in amounts that imply a marginal product of labor of 50 and a marginal product of capital of 100.
Do you know why the firm hired you? Explain.
Problem 5: American Tennis Shoe, Inc. is concerned because Congress has proposed an excise tax of $ 1 on each pair of tennis shoes sold in the United States. They are lobbying against the tax through an advertising campaign that says the tax will raise the price of tennis shoes by $1.
Using supply and demand graphs show how much of the tax will be passed on to the consumers.
Problem 6: Suppose you are an aide to a U. S. Senator who is concerned about the impact of a recently proposed excise tax on the welfare of her constituents. You explained to the Senator that one way of measuring the impact on her constituents is to determine how the tax change affects the level of consumer surplus enjoyed by her constituents. Based on your arguments, you are given the go ahead to conduct a formal analysis and obtained the following estimates of demand and supply: Qd = 500 – 5P and Qs = 2P – 60
a. Graph the supply and demand curves.
b. What is the equilibrium quantity and equilibrium price?
c. How much consumer surplus exists in the market?
d. If a $2 excise tax is levied on this good, what will happen to the equilibrium price and quantity?
e. What will the consumer surplus be after the tax?
Problem 7: The manager of a meat- packing plant can use either butchers (L) or meat saws (K) to prepare packages of sirloin steak. Based on estimates provided by an efficiency expert , the firm’s production function for sirloin steaks is given as: Q= K + L
a. Graph the isoquant corresponding to 5 units of output.
b. What is the marginal product of capital and labor? Does the answer depend on how much labor and capital are used?
c. If the price of labor is $ 2 per hour and the rental rate of capital is $ 3 per hour, how much of capital and labor should be used to minimize the costs of production?